Scale either equation (or both) with the goal of eliminating one of the variables
#[1] -10x + 7y = -2#
#[2] -4x - 15y = -1#
Multiply #[1]# by -2 and multiply #[2]# by 5
#[1'] -2(-10x + 7y = -2)#
#=> [1'] 20x -14y = 4#
#[2'] 5(-4x - 15y = -1)#
#=> [2'] -20x - 75y = -5#
#[1'] 20x -14y = 4#
#[2'] -20x - 75y = -5#
If we add both equations, #x# will be eliminated and we can solve for y
#[3] -89y = -1#
#=> y = 1/89#
To get #x#, substitute the obtained value for #y# in one of the equations #[1]#, #[1']#, #[2]#, #[2']#. For example, let's use #[1]#
#-10x + 7y = -2#
#=> -10x + 7(1/89) = -2#
#=:> -10x + 7/89 = -2#
#=> 10x = 2 + 7/89#
#=> 10x = (178 + 7)/89#
#=> 10x = 185/89#
#=> x = 37/178#
